Condorcet Voting

Purple is the Condorcet winner

Americans need an electoral system which represents the will of the people, not the slim margin of majority or—worse—the loudest voice of the plurality.  In every State and in our Presidential elections, Americans need an electoral system which represents the people as a whole, and not simply the side who turned out the most angry voters this year.  We need to elect by common consensus.

There is a concept called the Condorcet candidate, which is a Candidate who defeats all other Candidates in two-person races.

Each candidate in the Smith Set (top) defeats all of each candidate not in the Smith Set (bottom)
Each candidate in the Smith Set (top) defeats all of each candidate not in the Smith Set (bottom)

Consider Candidates A and B.  If, when using ranked ballots, more than half of those voters who rank at least one of A or B rank candidate A above some candidate B, then candidate A wins the race between A and B. If a particular candidate wins all such races between all other candidates, that is the Condorcet candidate.

The Smith Set is the smallest set of candidates who would themselves win a majority vote against each single candidate not in that set. If we remove all but one Smith candidate from an election, that candidate becomes the Condorcet candidate.

Voting Rules

Condorcet voting rules include Schulze, Tidemann’s Ranked Pairs, Benham Instant Runoff Vote, Tidemann’s Alternative Smith, and Tidemann’s Alternative Schwartz. Each rule has various strengths and weaknesses, and some are highly-complex or require determining how to measure the “strength” of a victory—either by number of votes or percentage win margin.

Benham IRV and Tidemann’s Alternative Smith and Schwartz strongly resist strategic voting and nomination.  Benham IRV simply elects the Condorcet winner or, if none exists, eliminates the candidate with the fewest votes and checks again. Tideman’s Alternative Smith elects the Condorcet candidate or, if there is none, eliminates all candidates outside the Smith set and then eliminates the one with the fewest votes, then repeats this process.

Tideman’s selecting from the Smith Set, also called a Condorcet Cycle. Notice the order of victories in the top cycle.

Tideman’s Alternative has the strongest resistance to manipulation and provides better representation: non-Smith candidates are rejected by the mutual majority, and Tideman’s Alternative eliminates them before identifying the weakest mutually-acceptable candidate. One could theoretically manipulate Benham IRV by splitting votes with a strong Smith-set candidate to create early elimination; and a non-Smith candidate can’t enter the Smith set by eliminating other candidates.

These rules force the election to the Condorcet candidate in cases where a system like plurality with run-off—including Instant Runoff Voting—fails. Such failure occurred when Burlington, VT implemented Instant Run-off Voting and elected neither the Plurality nor the Condorcet candidate. Constraint to the bona fide Condorcet candidate and to the Smith set prevents these failures and post-election controversy.